MHB Cardinality of a infinite subset

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The discussion centers on the cardinality of infinite sets and their subsets. It asserts that if a set has cardinality m, no subset can have a cardinality greater than m, which holds true even for infinite sets. The Cantor–Bernstein–Schroeder theorem supports this by stating that an injection from a set to a larger subset cannot exist. Additionally, while infinite sets can have injections into proper subsets, there remains a trivial injection from any subset to the original set. Clarification on the definition of cardinality m is requested for further understanding.
lamsung
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I saw the below statement which is intuitively correct:

If a set has cardinality m then none of its subsets has cardinality greater than m.

Is it necessarily true for a infinite set case?
 
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lamsung said:
If a set has cardinality m then none of its subsets has cardinality greater than m.

Is it necessarily true for a infinite set case?
Of course. If a subset $B$ of $A$ has cardinality strictly greater than the cardinality of $A$ itself, then there is an injection from $A$ to $B$, but not from $B$ to $A$, by the Cantor–Bernstein–Schroeder theorem. For an infinite setm, it is possible to have an injection into a proper subset, but there is also a trivial injection (inclusion) from a subset to the whole set.

If you need more details, tell us what $m$ is here and what is the definition in your context of having cardinality $m$ or greater than $m$.
 

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